An operational amplifier ("op amp") is an electronic circuit that amplifies an input signal differentially supplied between a noninverting input terminal and an inverting input terminal to produce an amplified output signal at an output terminal. An op amp is typically employed in an amplifier system having a feedback network connected between the output terminal (or simply "output") and one or both of the input terminals (or simply "inputs"). The gain in the negative feedback loop is -.mu..beta., where .mu. is the forward gain of the op amp, and .beta. is the gain of the feedback network.
When the input signal varies at some frequency, the output signal varies similarly. At low frequency, the two signals are substantially in phase. As frequency increases, the phase of the output signal falls progressively behind that of the input signal. The magnitude of the loop gain decreases. If the phase difference between the signals reaches 180.degree. while .vertline..mu..beta..vertline. is greater than 1, the feedback becomes positive. The system oscillates and is thus unstable.
The minimum acceptable stablility margin is considered to occur when the loop phase difference equals 135.degree. at the point where .vertline..mu..beta..vertline. is 1. Because the feedback network for a system utilizing an op amp is generally provided after op amp design is completed, the design is typically based on the "worst-case" assumption that .beta. is 1. This leads to the stability criterion that forward gain .mu. not roll off more than 9 dB/octave out to the unity-gain frequency.
An easy way to meet the preceding stability rule is with a single transconductance amplifier stage. Turning to the drawings, FIG. 1 illustrates a conventional bipolar differential stage A of this type. Input voltages V.sub.I+ and V.sub.I-, whose difference is amplifier input signal V.sub.I, are respectively supplied to the noninverting and inverting inputs of stage A. Its noninverting output provides amplifier output voltage V.sub.O.
The frequency response of stage A is largely determined by a single dominant pole dependent on the parasitic capacitance CP at the output. FIG. 2 shows asymptotes for how .mu. varies with frequency f for stage A. The gain drops 6 dB/oct. as the frequency f.sub.o of the dominant pole is passed and then 6 dB/oct. more as the higher pole frequency f.sub.L that limits the bandwidth is passed. Bandwidth-limiting frequency f.sub.L, which is a characteristic of the overall amplifier system and cannot readily be altered, occurs beyond unity-gain frequency f.sub.U. Stage A thereby automatically satisfies the stability criterion. Unfortunately, the maximum gain is typically on the order of 40 dB. This is much too low for many applications.
The gain can be increased by cascading two amplifier stages A.sub.I and A.sub.O as shown in FIG. 3. Output stage A.sub.O functions as an inverter. A capacitor C connected across stage A.sub.O provides frequency compensation for the amplifier.
FIG. 4 shows a typical asymptotic frequency response for the two-stage amplifier in FIG. 3. Two dominant poles, represented by pole frequencies f.sub.O and f.sub.I which respectively depend on the parasitic capacitances at the A.sub.O and A.sub.I outputs, largely determine the frequency characteristics. The gain roll-off increases 6 dB/oct. in passing each of frequencies f.sub.O, f.sub.I, and f.sub.L. The upper curve in FIG. 4 shows how the asymptotic frequency response would appear if capacitor C were absent. The lower curve shows the actual compensated asymptotic response.
In the absence of capacitor C, the combination A.sub.I and A.sub.O would not meet the stability rule because .mu. drops 12 dB/oct. between f.sub.I and the unity-gain frequency. Capacitor C splits the dominant poles further, causing f.sub.I to move beyond the unity-gain point. The gain asymptotically rolls off at a straight 6 dB/oct. between f.sub.O and f.sub.U so that the amplifier meets the stability criterion. The maximum gain of approximately 80 dB is an improvement. However, .mu. is still too low for many applications.
Three or more amplifier stages can be placed in cascade to increase the gain further. While providing frequency compensation for such a device has generally been a complex process, U.S. Pat. No. 4,559,502 ("US 502") describes an elegant capacitive-nesting solution to the problem. FIG. 5 illustrates a three-stage amplifier disclosed in US 502.
The prior art amplifier in FIG. 5 is formed with input, intermediate, and output transconductance stages A.sub.I, A.sub.M, and A.sub.O. Stages A.sub.I and A.sub.M function as noninverters. Stage A.sub.O again functions as an inverter. The A.sub.I noninverting output is connected to the noninverting input of stage A.sub.M whose noninverting output is connected to the noninverting input of stage A.sub.O. Its output is an inverting output.
For convenience in later making a comparison to the present invention, the "noninverting" and "inverting" labels used here for the A.sub.O inputs and output in FIG. 5 are actually opposite to those employed in US 502. However, this does not affect the function of stage A.sub.O whose output voltage V.sub.O is still inverted relative to the A.sub.O input signal difference.
The capacitive nesting in FIG. 5 begins with the amplifier portion consisting of stages A.sub.M and A.sub.O. A capacitor C1 is connected between the noninverting input of stage A.sub.O and its inverting output. The value of capacitor C1 is selected to make the portion A.sub.M and A.sub.O satisfy the stability rule. The frequency compensation is completed by connecting a capacitor C2 between the A.sub.M noninverting input and the A.sub.O inverting output. Capacitor C2 is chosen to have such a value that the combination of stage A.sub.I with portion A.sub.M and A.sub.O likewise satisfies the stability criterion.
Turning to FIG. 6 it depicts a typical version of the asymptotic frequency response for the amplifier of FIG. 5. The frequency characteristics are controlled by the two dominant poles represented by pole frequencies f.sub.O and f.sub.I (as described above) plus a third dominant pole represented by pole frequency f.sub.M dependent on the parasitic capacitance at the A.sub.M output. In the absence of capacitors C1 and C2, the gain roll-off at the unity-gain point would be far too much to satisfy the stability rule. See the upper curve in FIG. 6.
Insertion of capacitor C1 causes poles f.sub.O and f.sub.M to be split further apart. See the intermediate curve in FIG. 6. Insertion of capacitor C2 then splits poles f.sub.O and f.sub.I. The lower curve in FIG. 6 shows the final compensated response. Lower pole f.sub.O has moved from starting point f.sub.OS to lower final point f.sub.OF. Higher poles f.sub.I and f.sub.M have moved from starting points f.sub.IS and f.sub.MS to higher final points f.sub.IF and f.sub.MF beyond f.sub.U. The asymptotic gain roll-off is an acceptable straight 6 dB/oct. all the way out to f.sub.U.
FIG. 6 illustrates typical values that f.sub.I, f.sub.M f.sub.O, f.sub.U, and f.sub.L might have in the amplifier of FIG. 5. These numerical values are not disclosed in US 502 but are presented solely for later comparison with the present invention.
Note that poles f.sub.I and f.sub.M are separated from each other by approximately a factor of two in the final compensated amplifier. In particular, f.sub.IF is one half of f.sub.MF in FIG. 6. This separation results from usage of capacitor C2 and is needed to prevent the amplifier from going into resonance. Unfortunately, the separation leads to a factor-of-two reduction in frequency bandwidth. Providing the amplifier with additional nests to increase the gain further likewise reduces the bandwidth by an additional factor of two for each additional nest. A frequency-compensation technique that employs the basic capacitive-nesting principle of US 502, but overcomes the bandwidth loss that occurs because of capacitor C2, would be quite advantageous.
German Patent Publication 3829135 A1 ("German 135") describes a noteworthy approach to the matter of achieving high gain without significantly losing bandwidth. In German 135, the amplifier input signal is provided to two or more differential input stages connected in parallel. One of the input stages has a low gain and high bandwidth, while another has a high gain and a low bandwidth. Each remaining input stage (if any) has an intermediate gain and an intermediate bandwidth. The amplified output signals of the input stages are combined and supplied to a current-amplifying output stage that provides the amplifier output signal.
German 135 states that frequency compensation need only be supplied for the input stage having the high bandwidth and low gain. While this may be true, German 135 seems to lack the advantageous straight 6 dB/oct. asymptotic gain roll-off between the lowest dominant pole frequency and the unity-gain point. In the preferred example, the frequency compensation for part of the frequency range is apparently achieved with a single capacitor connected across the input stages. German 135 does not use anything like capacitive nesting.